- Dimensional analysis.
- Curvilinear coordinate systems.
- Nonlinear systems of ordinary differential equations (equilibrium points, stability theory)
- Perturbation methods.Boundary layer analysis.
- Wave solutions of partial differential equations (travelling waves, standing waves, shock waves, solitons).
- Green functions.
- Implementation of various methods using symbolic packages.
- Applications to civil engineering problems.
Applied mathematics
| Code | GPOL_A_16113 |
|---|---|
| Instructor | PETROPOULOU EUGENIA |
| eclass | https://eclass.upatras.gr/courses/CIV1555/ |
| Mandatory/Optional | Elective |
| Credits ECTS | 7,5 |
| COURCE OUTLINE | https://www.civil.upatras.gr/wp-content/uploads/2021/11/GPOL_A_16113-Applied_Mathematics-_EN.docx |
It is the main course through which students come into contact with specific mathematical methodologies, with the help of which they can study variousproblems related to the science of Civil Engineering, such as problems of oscillations, deformations, hydraulics, wave propagation, traffic, etc.In particular, they are introduced in dimensional analysis, qualitative methods for the study of nonlinear systems of differential equations, approximate methods for solving nonlinear differential equations and advanced analytical methods for solving differential equations.In addition, several methodologies are implemented using packages of symbolic calculations.
Upon successful completion of the course, students will be able to
- Recognize problems in the science of civil engineering that can be addressed using specific mathematical methodologies.
- Use dimensional analysis to study various problems in the science of civil engineering and to extract useful information.
- Study qualitatively nonlinear systems of differential equations
- Solve differential equations, linear and non-linear, ordinary or partial, using approximate methods or advanced analytical methods
Use symbolic calculation packages to implement the mathematical methodologiestaught during the course.
